Bicycle Riding on Square Wheels

Roland Piquepaille writes "Before starting our long working week, let's relax with this story of a bicycle with square wheels. No, it's not a joke. And it even rides smoothly. But there is a trick: the road must have a specific shape. The Math Trek section of Science News Online tells us more about this strange bicycle -- actually a tricycle with two front wheels and one back wheel. Read this overview for some excerpts and a picture of the tricycle, or the original article for an additional animation."

Comments

The answer is - A circle!

[DR SoB]

The question at the bottom that states they don't have a wheel the same shape as the surface, I tend to disagree, wouldn't a common circular wheel, while going over a steep hill both be circular shapes? What about tank tracks? They are both flat? A flat wheel and a flat surface = the same!

Web design with Mathematica?!?

[Just Some Guy]

If you follow the link to the designer's own web page, and scroll to the bottom, you see:

Created by Mathematica (February 3, 2004)

I just realized that any geek cred I thought I had was just an illusion. I don't ever want to hear jokes about Emacs again. Understand?

Tricycle sounds like the Dymaxion Car

[G4from128k]

That backwards tricycle sounds like the Buckminster Fuler's Dymaxian Car. That beast was designed for minimum air resistance. Also having the two wheels in front provides better stability when cornering during hard braking. Still, tricycles do have some roll-over stability problems because the CG is closer to the sides of the wheelbase.

Duh, physics class 101

[192939495969798999]

Every college physics class has one day where they talk about this,where the road is lumpy in a specific way, and then the bicycle with square wheels can drive. You know what else has a smooth ride? the space shuttle crawler. If you weigh enough, you just crush anything that would otherwise be a bump. I'll be happy when I see a vehicle besides a tank whose method of ground contact changes shape to accommodate for the road (i.e. tank tread on a bicycle). That would be sweet!

http://www.fulcrumgallery.com

Reminds me of the british 20p coin

[Funkitup]

This coin has 7 sides so you wouldn't expect it to roll smoothly.

However, they are cleverly made so that the diameter is equal right the way around the coin. Therefore, since the center of mass doesn't move, the coin will roll smoothly in slot machines etc. Try it!

I'm not sure whether the 50p is the same or not. I don't have one in my wallet to test as I used it to buy a packet of wine gums...

MMmmmm wine gums...

It's open to the public -- you can go ride it!

[melquiades]

I believe it's still sitting in the basement-level lobby of the Olin/Rice building at Macalester. You can just walk up and give it a ride.

In practice, it doesn't work perfectly: the wheels slip a bit on the upslope. But if you get a bit of speed, it rolls along nicely! Quite fun.

Reuleaux Triangle

[ortholattice]

Also neat is the Reuleaux Triangle that is not round but even so has a constant width as it rotates. If it is used as a roller between two planks, it will roll smoothly and the distance between the planks will remain constant. This java applet demonstrates it.

huge nitpick: you are both wrong

[mattyp]

movement of the center of mass nor axle has anything to do with smoothness: it's movement of the rider.

20 or 30 years ago (i searched the web, sorry, couldn't find) honda (an engineer there, for an internal contest) built a bicycle with square wheels that rode smoothly on a flat surface. It worked with a cam on the swingarm, so the axle could move up and down while rolling, and the bike frame (and rider) stayed level. I'm sure the center of mass also moved.

Re:Allrighty then

[merlin_jim]

Actually, this research does have real world applications.

In the early parts of the industrial age it was found that a certain shape of gear teeth (both along the axle of the gear, and the tooth's profile seen edge on), removed gear slip allowing for much smoother operation, to the point where bevelled gears are used in all car transmissions today.

This research may lead to innovative and new ways to mesh gears together; for instance, I could imagine one application to allow gears with teeth numbers that aren't strictly in ratio to their diameters to mesh properly. If that were the case, then we could make transmissions and gear boxes an order of magnitude or so smaller...